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Register a new userThermodynamics of a weakly interacting Bose gas above the transition temperature
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We study thermodynamic properties of weakly interacting Bose gases above the transition temperature of Bose-Einstein condensation in the framework of a thermodynamic perturbation theory. Cases of local and non-local interactions between particles are analyzed both analytically and numerically. We obtain and compare the temperature dependencies for the chemical potential, entropy, pressure, and specific heat to those of noninteracting gases. The results set reliable benchmarks for thermodynamic characteristics and their asymptotic behavior in dilute atomic and molecular Bose gases above the transition temperature.
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We prepare a chemically and thermally one-dimensional (1d) quantum degenerate Bose gas in a single microtrap. We introduce a new interferometric method to distinguish the quasicondensate fraction of the gas from the thermal cloud at finite temperature. We reach temperatures down to $kTapprox 0.5hbaromega_perp$ (transverse oscillator eigenfrequency $omega_perp$) when collisional thermalization slows down as expected in 1d. At the lowest temperatures the transverse momentum distribution exhibits a residual dependence on the line density $n_{1d}$, characteristic for 1d systems. For very low densities the approach to the transverse single particle ground state is linear in $n_{1d}$.
We study the thermodynamics near the generic (density-driven) superfluid--Mott-insulator transition in the three-dimensional Bose-Hubbard model using the nonperturbative renormalization-group approach. At low energy the physics is controlled by the Gaussian fixed point and becomes universal. Thermodynamic quantities can then be expressed in terms of the universal scaling functions of the dilute Bose gas universality class while the microscopic physics enters only {it via} two nonuniversal parameters, namely the effective mass $m^*$ and the scattering length $a^*$ of the elementary excitations at the quantum critical point between the superfluid and Mott-insulating phase. A notable exception is the condensate density in the superfluid phase which is proportional to the quasi-particle weight $Zqp$ of the elementary excitations. The universal regime is defined by $m^*a^*{}^2 Tll 1$ and $m^*a^*{}^2|deltamu|ll 1$, or equivalently $|bar n-bar n_c|a^*{}^3ll 1$, where $deltamu=mu-mu_c$ is the chemical potential shift from the quantum critical point $(mu=mu_c,T=0)$ and $bar n-bar n_c$ the doping with respect to the commensurate density $bar n_c$ of the T=0 Mott insulator. We compute $Zqp$, $m^*$ and $a^*$ and find that they vary strongly with both the ratio $t/U$ between hopping amplitude and on-site repulsion and the value of the (commensurate) density $bar n_c$. Finally, we discuss the experimental observation of universality and the measurement of $Zqp$, $m^*$ and $a^*$ in a cold atomic gas in an optical lattice.
We study the localization properties of weakly interacting Bose gas in a quasiperiodic potential commonly known as Aubry-Andre model. Effect of interaction on localization is investigated by computing the `superfluid fraction and `inverse participation ratio. For interacting Bosons the inverse participation ratio increases very slowly after the localization transition due to `multisite localization of the wave function. We also study the localization in Aubry-Andre model using an alternative approach of classical dynamical map, where the localization is manifested by chaotic classical dynamics. For weakly interacting Bose gas, Bogoliubov quasiparticle spectrum and condensate fraction are calculated in order to study the loss of coherence with increasing disorder strength. Finally we discuss the effect of trapping potential on localization of matter wave.
Using a multiple-image reconstruction method applied to a harmonically trapped Bose gas, we determine the equation of state of uniform matter across the critical transition point, within the local density approximation. Our experimental results provide the canonical description of pressure as a function of the specific volume, emphasizing the dramatic deviations from the ideal Bose gas behavior caused by interactions. They also provide clear evidence for the non-monotonic behavior with temperature of the chemical potential, which is a consequence of superfluidity. The measured thermodynamic quantities are compared to mean-field predictions available for the interacting Bose gas. The limits of applicability of the local density approximation near the critical point are also discussed, focusing on the behavior of the isothermal compressibility.
We analyze the two-body momentum correlation function for a uniform weakly interacting one-dimensional Bose gas. We show that the strong positive correlation between opposite momenta, expected in a Bose-Einstein condensate with a true long-range order, almost vanishes in a phase-fluctuating quasicondensate where the long-range order is destroyed. Using the Luttinger liquid approach, we derive an analytic expression for the momentum correlation function in the quasicondensate regime, showing (i) the reduction and broadening of the opposite-momentum correlations (compared to the singular behavior in a true condensate) and (ii) an emergence of anticorrelations at small momenta. We also numerically investigate the momentum correlations in the crossover between the quasicondensate and the ideal Bose-gas regimes using a classical field approach and show how the anticorrelations gradually disappear in the ideal-gas limit.
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